Strong Asymptotics of Planar Orthogonal Polynomials: Gaussian Weight Perturbed by Finite Number of Point Charges

30 Mar 2020 Lee Seung-Yeop Yang Meng

We consider the planar orthogonal polynomial $p_{n}(z)$ with respect to the measure supported on the whole complex plane $${\rm e}^{-N|z|^2} \prod_{j=1}^\nu |z-a_j|^{2c_j}\,{\rm d} A(z)$$ where ${\rm d} A$ is the Lebesgue measure of the plane, $N$ is a positive constant, $\{c_1,\cdots,c_\nu\}$ are nonzero real numbers greater than $-1$ and $\{a_1,\cdots,a_\nu\}\subset{\mathbb D}\setminus\{0\}$ are distinct points inside the unit disk. In the scaling limit when $n/N = 1$ and $n\to \infty$ we obtain the strong asymptotics of the polynomial $p_n(z)$... (read more)

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